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This article is cited in 2 scientific papers (total in 2 papers)
Finiteness of a $3$-generated lattice with seminormal and coseminormal elements among generators
M. P. Shushpanov El'tsyn Ural Federal University, ul. Mira 19, Yekaterinburg, 620002 Russia
Abstract:
It is known that a modular $3$-generated lattice is always finite and contains at most 28 elements. Lattices generated by three elements with certain modularity properties may no longer be modular but nevertheless remain finite. It is shown that a $3$-generated lattice among generating elements of which one is seminormal and another is coseminormal is finite and contains at most 45 elements. This estimate is stated to be sharp.
Keywords:
left-modular element, right-modular element, seminormal element, defining relation.
Received: 25.11.2016 Revised: 23.02.2017
Citation:
M. P. Shushpanov, “Finiteness of a $3$-generated lattice with seminormal and coseminormal elements among generators”, Algebra Logika, 57:3 (2018), 362–376; Algebra and Logic, 57:3 (2018), 237–247
Linking options:
https://www.mathnet.ru/eng/al854 https://www.mathnet.ru/eng/al/v57/i3/p362
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Abstract page: | 142 | Full-text PDF : | 15 | References: | 24 | First page: | 3 |
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